Historical evolution of eddy viscosity models in large eddy simulation of turbulent flows

Due to the complexity of turbulent flows, it is not possible to solve the governing equations in full detail. Therefore, different numerical approaches have been proposed to solve the governing equations and analyze the flow characteristics. The most important methods include Direct Numerical Simulation (DNS), Large Eddy Simulation (LES) and Reynolds Averaged Navier-Stokes Equations (RANS). In terms of accuracy and computational cost, large eddy simulation is in between two other methods. In this method, large and small scales are separated by applying a low-pass filter. Large scales are solved and small scales are modeled. So far, various models have been presented for small or subgrid scales. Eddy viscosity models are the most common models used for this purpose. The first and simplest eddy viscosity model is the standard Smagorinsky model. The accuracy of this model is low, especially for complex geometries. Therefore, various studies have been conducted to increase the accuracy of this model. The dynamic Smagorinsky model, dynamic localization model, and scale-dependent dynamic model are among the most widely used models. In this paper, the progress of eddy viscosity models used in large eddy simulation is presented.